The entire essay is hyperbolic, from his description of the squalid conditions of the peasants and their anticipated reaction to the proposal, to the narrator's cold detachment to the actual plight of these people, which is assumed to be the callousness of the upper class and the backlash of political posturing.

The essay is satirical of the type of deranged logic that comes from social detachment from people of lower social classes. His proposal is to eat children, and yet he claims that a great benefit of this is "that it will prevent those voluntary abortions, and that horrid practice of women murdering their bastard children, alas! too frequent among us! sacrificing the poor innocent babes I doubt more to avoid the expense than the shame, which would move tears and pity in the most savage and inhuman breast."

So murder by the state is OK, because it benefits the upper class and relieves the hunger of the lower class, but things like emotions and moral obligations are not seen as a quality belonging to the lower class, so their abortions are little more than the act of savages.

Hyperbole is exaggeration. Swift, fed up with the rejection of his commonsense solutions to problems of poverty, creates a narrator who, in an exaggerated way, is only capable of seeing people in terms of profit.

Examples of hyperbole start with the narrator’s proposal to fatten, raise and butcher human babies, both to help the poor become self-supporting and to enrich Ireland. Swift mercilessly exaggerates the narrator’s unconscious tendency to dehumanize others. The narrator writes, for example: “I rather recommend buying the Children alive, and dressing them hot from the Knife, as we do roasting Pigs.” Such vivid, hyperbolic detail elevates the shock value of treating humans as commodities and illustrates that Swift’s narrator lacks empathy. This humor, dark as it is, comes from the slippage between the narrator’s “dollars and cents” approach to people and the reader’s larger moral awareness. Swift uses hyperbole to persuade us to turn against the narrator’s narrow “profit and loss” mentality.

Brene Brown’s short video on empathy can help with understanding that the narrator looks down from above at people in trouble, whereas Swift invites us to embrace people in their full humanity.

Swift’s style is hyperbolic from the very beginning of the essay, in which he lays out the social problem that he wishes to address, the treatment of the poor in England:

These mothers instead of being able to work for their honest livelihood, are forced to employ all their time in stroling to beg sustenance for their helpless infants who, as they grow up, either turn thieves for want of work, or leave their dear native country, to fight for the Pretender in Spain, or sell themselves to the Barbadoes.

The hyperbole (extreme exaggeration) here is in the emphasis. He says that poor mothers spend “all their time” begging for food and money. He also says that the children of these poor women all come to one of three ends: they either become thieves, leave England to fight for Spain, or sell themselves into slavery.

This emphasis is necessary for Swift to set up his satire, because it portrays the attitude of the upper-class English as snobbish and discriminatory.

The following line demonstrates Swift’s humor:

I grant this food will be somewhat dear, and therefore very proper for landlords, who, as they have already devoured most of the parents, seem to have the best title to the children.

Swift is saying here that once the infants are for sale as food, the landlords will deserve the first opportunity to buy and eat them, as they have already caused so many of their parents to be “devoured.” It is the word “devoured” that creates the humor. As satire, Swift does not mean it literally. Instead, he is referring to the practice of punishing or imprisoning those who cannot pay their rent, as was the case with many of the urban poor in England at that time.

In short, Swift doesn't want us to eat babies. He used the example as an extreme and dramatic overstatement to shed light on the severity of the potato famine. All these years later, it's worked and has become known as one of the greatest pieces of satire in history.